Information on Result #686797
Linear OA(837, 32780, F8, 8) (dual of [32780, 32743, 9]-code), using construction X4 applied to Ce(8) ⊂ Ce(5) based on
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(826, 32768, F8, 6) (dual of [32768, 32742, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(811, 12, F8, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,8)), using
- dual of repetition code with length 12 [i]
- linear OA(81, 12, F8, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(838, 32781, F8, 8) (dual of [32781, 32743, 9]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(837, 32780, F8, 2, 8) (dual of [(32780, 2), 65523, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(837, 32780, F8, 3, 8) (dual of [(32780, 3), 98303, 9]-NRT-code) | [i] | ||
| 4 | Digital (29, 37, 32780)-net over F8 | [i] | ||
| 5 | Linear OOA(837, 16390, F8, 2, 8) (dual of [(16390, 2), 32743, 9]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(837, 8195, F8, 8, 8) (dual of [(8195, 8), 65523, 9]-NRT-code) | [i] | OA Folding and Stacking | |